Related papers: The Full Strategy Minority Game
A key challenge in multi-agent systems is the design of intelligent agents solving real-world tasks in close interaction with other agents (e.g. humans), thereby being confronted with a variety of behavioral variations and limited knowledge…
Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which constructs such a perfect strategy or refutes its…
We propose a new model of minority game with so-called smart agents such that the standard deviation and the total loss in this model reach the theoretical minimum values in the limit of long time. The smart agents use trail and error…
We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform…
Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…
A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions…
We discover the mechanism for the transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with a statistical mechanics analysis…
This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…
Many real-world applications involve some agents that fall into two teams, with payoffs that are equal within the same team but of opposite sign across the opponent team. The so-called two-team zero-sum Markov games (2t0sMGs) can be…
Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive…
We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, $N$ agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off…
We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor…
Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…
Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…
Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…
We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…
This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters…
Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…
We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such…
In this work we present a pedagogical introduction to the minority game and various new versions of it with interesting properties, focusing in its applications in socialphysics. For instance, some systems display a kind of social behavior…